Dynamical Transition and Bifurcation of Hydromagnetic Convection in a Rotating Fluid Layer

Li, Liang; Fan, Yanlong; Han, Daozhi; Wang, Quan

doi:10.2139/ssrn.3970809

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2022

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“…The understanding of the asymptotic behavior of dynamical systems is one of the most important problems of modern mathematical physics(see,e.g. [14,21] and references therein). One way to treat this problem is to analyse the existence of its global attractor.…”

Section: Introductionmentioning

confidence: 99%

Global Attractors for a Class of Weakly Damped Wave Equations with Gradient Type Nonlinearity

Pan

Wang

Shuai

2022

J Nonlinear Math Phys

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In this paper, the main purpose is to study existence of the global attractor for the weakly damped wave equation with gradient type nonlinearity. To this end, we first verify the existence and uniqueness of global weak solution by the Galerkin method and compulsively variational method. Furthermore, we obtained the global strong solution under some mild assumptions on f. Secondly, we utilize the $$\omega$$ ω -limit compactness to show the semigroup generated by the equation has a compact, connected and invariant attractor.

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Section: Introductionmentioning

confidence: 99%